Southwest Co-op produces bags of fertilizer, and it is concerned about impurity content. It is believed that the weights of impurities per bag are normally distributed with a mean of 12.2 grams and a standard deviation of 2.8 grams. A bag is chosen at random.
a. What is the probability that it contains less than 10 grams of impurities?
b. What is the probability that it contains more than 15 grams of impurities?
c. What is the probability that it contains between 12 and 15 grams of impurities?
d. It is possible, without doing the detailed calculations, to deduce which of the answers to parts (a) and (b) will be the larger. How would you do this?

a) 0.216

b) 0.1587

c) 0.369

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 12.2 grams

Standard Deviation, σ = 2.8 grams

We are given that the distribution of weights of impurities per bag is a bell shaped distribution that is a normal distribution.

Formula:

a) P(contains less than 10 grams of impurities)

P(x < 10)

Calculation the value from standard normal z table, we have,  

b) P(contains more than 15 grams of impurities)

P(x > 15)

Calculation the value from standard normal z table, we have,  

c) P(contains between 12 and 15 grams of impurities)

d) The mean divide the data in exactly two parts. Since 15 is farther away from the mean as compared to 10, the probability obtained in part (b) is smaller as compared to probability obtained in part (a).

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3

this answer is !